Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
from sys import stdin

num = int(stdin.readline().strip())
t,i = [0],1
while t[i-1]<num:
  t.append(t[-1]+i)
  i += 1
i,found = 1,False
while not(found) and t[i]<<1<=num:
  target,low,hi = num-t[i],i,len(t)
  while not(found) and low+1!=hi:
    mid = low+((hi-low)>>1)
    if t[mid]==target:
      found = True
    elif t[mid]>target:
      hi = mid
    else:
      low = mid
  found = found or t[low]==target
  i += 1
if found:
  print('YES')
else:
  print('NO')